Large Deviations for the Infinite Server Queue in Heavy Traffic

In this paper, we establish large deviations approximations to the tail probabilities of the queue-length r.v. in an infinite-server queue in heavy traffic. These large deviations approximations complement the existing Gaussian approximations developed for such systems using weak convergence theory of function spaces. We also describe a simulation-based algorithm for numerical computing such tail probabilities that take advantage of the large deviations theory developed here.